How do you differentiate #f(x)=1/x*e^(x^2)# using the product rule?
1 Answer
Jan 25, 2016
# f'(x) = e^(x^2) (2 - 1/x^2 ) #
Explanation:
Differentiate using ' product rule' and 'chain rule'.
rewrite f(x) =
#x^-1 . e^(x^2) # f'(x)
#= x^-1 . d/dx (e^(x^2)) + e^(x^2) . d/dx ( x^-1 ) #
# = x^-1 . e^(x^2) .d/dx (x^2 ) + e^(x^2) .(- x^-2 )#
# = x^-1 . e^(x^2) .(2x ) - x^-2 . e^(x^2) #
# = 1/cancel(x) . 2cancel(x). e^(x^2) - 1/x^2 . e^(x^2) #
#= e^(x^2) ( 2 - 1/x^2 ) #
